Yeast is one of the most commonly used ways to leaven baking. Yeast converts the sugars naturally occurring in the flour into gases which leaven the dough.
Commercial Bakers often use compressed cakes of yeast, also known as "Baker's" or "Fresh" yeast. Fresh yeast dissolves easily in dough and it is very dependable. You crumble the necessary quantity (usually measured by weight) but it does require rehydration, a process known as "proofing". Warm water is added to the yeast and left to sit until the yeast is awakened and air bubbles appear ensuring your yeast is alive. However, Fresh yeast does have a limited shelf life and must be kept in the refrigerator.
Active Dry (or "Traditional") yeast does not need to be refrigerated. This yeast consists of live yeast covered with a coating of dead yeast cells. Traditional yeast also needs to be proofed to ensure the inactive yeast has been reactivated.
Within the last 40 years improvements in the manufacturing process allowed for the development of Instant Yeast. It eliminated the need for hydration while still maintaining and actually increasing the fermentation power. The finer granules of dried yeast should be mixed directly into the flour and are easily dissolved in the dough without proofing. Instant yeast also behaves more consistently than Traditional yeast and is commonly used in bread machines.
Rapid Rise yeast is a version of Instant yeast with additional chemicals (ascorbic acid) added to speed up the fermentation process even more.
Although the type of yeast is not interchangeable in all recipes, generally you can replace Traditional with Instant by using slightly less. Traditional can be replaced with Fresh by using about twice as much.